Apparatus and method for determination of stroke volume using the brachial artery

ABSTRACT

Provided herein are methods and apparatus for stroke volume determination by bioimpedance from a patient&#39;s upper arm, or brachium, or a patient&#39;s thorax, utilizing pulsations of the arteries contained therein. The apparatus includes two or more spaced apart alternating current flow electrodes positioned on the patient&#39;s arm or thorax and two or more spaced apart voltage sensing electrodes positioned on the patient&#39;s arm or thorax and in-between alternating current flow electrodes. The system and method utilizes the mean value of the second time-derivative of the cardiogenically induced impedance variation of the patient using the measured voltage from the voltage sensors in calculating the stroke volume of the patient.

This application is a continuation-in-part of U.S. application Ser. No.10/870,281, filed Jun. 16, 2004, and claims priority from U.S.Provisional Patent Application No. 60/634,616, filed Dec. 8, 2004.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This present invention relates to the determination of the volumetricoutput of the left ventricle of a person's heart per beat, known asstroke volume (SV) (mL), and, the volumetric output of a person's heartper minute, otherwise known as the cardiac output (CO) (L/Min). Moreparticularly, this invention relates to the determination of SV and COby transbrachial electrical bioimpedance.

2. Background Information

All methods, apparatus and inventions related to the measurement ofSV/CO by the electrical bioimpedance method have heretofore beenimplemented either by the transthoracic method, also known astransthoracic or thoracic electrical bioimpedance plethysmography (orcardiography), or by total body (whole body) electrical bioimpedanceplethysmography, also known as whole body electrical bioimpedancecardiography (Moshkovitz Y, et al. Curr Opin Cardiol 2004; 19:229-237).Apart from a velocimetric method and apparatus described by Bernstein etal. (U.S. Pat. No. 6,511,438 B2), all prior art assumes aplethysmographic origin for the measured impedance change with respectto time (ΔZ(t)), and its peak rate of change (dZ/dt_(max)), coincidingwith each beat of the heart (Moshkovitz Y, et al. Curr Opin Cardiol2004; 19:229-237). The plethysmograghic-based transthoracic SV equationsused clinically basically comprise two methods; they are described inU.S. Pat. No. 6,511,438 B2, and are known as the Nyboer-Kubicek equation(Kubicek equation) and the Sramek-Bernstein equation. The deficienciesof the method and apparatus invented by Bernstein et al., disclosed inU.S. Pat. No. 6,511,438 B2, include the following:

-   -   1. A volume conductor, V_(c), which underestimates the        intrathoracic blood volume (ITBV) by approximately 15-20%    -   2. The implementation of a square root function for heart rate        (H.R.) frequency (i.e. √{square root over        (f)}₀=1/(T_(RR))^(0.5)=(H.R./60)^(0.5)) which is superfluous and        unnecessary.    -   3. A best method in the preferred embodiment for determining        left ventricular ejection time, T_(lve), is not disclosed.    -   4. A best method in the preferred embodiment for determining        point B is not disclosed    -   5. A best method in the preferred embodiment for determining        dZ/dt_(max), based on the accurate determination of point B, is        not disclosed

There are numerous drawbacks to the current methods and apparatus usedfor measurement of the transthoracic electrical bioimpedance strokevolume parameters. What is needed is an alternative approach to thetransthoracic electrical bioimpedance determination of stroke volume;specifically, an alternative site for signal acquisition, and bettermethods to measure the independent variables comprising the strokevolume equation.

SUMMARY OF THE INVENTION

The present invention is an apparatus for determining stroke volume bybioimpedance from a patient, including two or more spaced apartalternating current flow electrodes positionable on a patient, two ormore spaced apart voltage sensing electrodes positionable on the patientand between the alternating current flow electrodes, an alternatingcurrent source electrically connected to the alternating current flowelectrodes, a voltmeter electrically connected to the voltage sensingelectrodes, and a processing unit in communication with the voltagesensing electrodes. The processing unit is capable of using a voltagesensed by the voltage sensing electrodes to calculate a mean value of asecond time-derivative of a cardiogenically induced impedance variationof the patient and to determine therefrom a stroke volume of thepatient.

In another aspect of the present invention, a method of determiningstroke volume by bioimpedance from a patient includes positioning two ormore spaced apart alternating current flow electrodes on a patient,positioning two or more spaced apart voltage sensing electrodes on thepatient and between the alternating current flow electrodes, providingan alternating current flow (I(t)) through the electrically conductiveelectrodes creating a current field, measuring a voltage (U(t)) betweenthe voltage sensing electrodes within the current field, calculating amean value of a second time-derivative of a cardiogenically inducedimpedance variation of the patient using the measured voltage (U(t)),and calculating the stroke volume (SV) of the patient using thecalculated second time-derivative mean value.

Other objects and features of the present invention will become apparentby a review of the specification, claims and appended figures.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings accompanying and forming part of this specification areincluded to depict certain aspects of the invention. A clearerconception of the invention, and of the components and operation ofsystems provided with the invention, will become more readily apparentby referring to the exemplary, and therefore nonlimiting, embodimentsillustrated in the drawings, wherein identical reference numeralsdesignate the same components. The invention may be better understood byreference to one or more of these drawings in combination with thedescription presented herein. It should be noted that the featuresillustrated in the drawings are not necessarily drawn to scale.

FIG. 1 shows placement of electrodes on a patient. A.C.(I) is injectedthrough a segment of the upper arm, otherwise known as the brachium, theboundaries of which are the deltoid muscles of the shoulder and axillaproximally, and the elbow and antecubital fossa distally. Embeddedwithin the brachial musculature and connective tissue, and anatomicallysituated medial to the brachial bone, otherwise known as the humerus, isthe brachial artery. The upper arm, including the connective tissue,bone, nervous tissue, veins, and the brachial artery comprise anaggregate impedance (Z) to current flow. The passage of A.C across thebrachium generates a quasi-static voltage, (U₀), and, concordant withevery pressure pulse of the brachial artery, a time-dependent drop involtage, (ΔU(t)), this pressure pulse following every onset of leftventricular ejection with a short time delay.

FIG. 2 shows an example of ECG, ΔZ(t) (Ω) and dZ/dt (Ω/s²) waveformsobtained transthoracically from a human subject, where T_(RR)=the R-Rinterval, or the time for one cardiac cycle (seconds, s); Q=onset ofventricular depolarization; ---------=maximum systolic upslopeextrapolation of ΔZ(t); B=aortic valve opening; C=peak rate of change ofthe thoracic cardiogenic impedance variation, dZ/dt_(max) (Ω/s²);X=aortic valve closure; Y=pulmonic valve closure; O=rapid ventricularfilling wave; Q-B interval=pre-ejection period, T_(PE) (seconds, s); B-Cinterval=time-to-peak dZ/dt, TTP (seconds, s); B-X interval=leftventricular ejection period, T_(LVE) (seconds, s). dZ/dt waveform to theright shows dZ/dt_(max) remaining constant throughout the ejectioninterval, T_(LVE), which represents outflow compensation.

FIGS. 3 a and 3 b show the relationship between the dZ/dt curve and thedP/dt or d(SpO₂)/dt curve. FIG. 3 a further shows an example wherepoints B and X are apparent on the dZ/dt curve and FIG. 3 b shows anexample where point B is not detectable, but point X is detectable onthe dZ/dt curve.

FIG. 4 shows the primary waveforms of ΔSpO₂(t) and/or ΔP(t), aligned intime with the dZ/dt waveform.

FIG. 5 shows an example where points B and X are distinguishable andthat point B corresponds with aortic valve opening (AVO) on the firsttime-derivatives of either the ΔSpO₂(t)or ΔP(t) waveforms and point Xcorresponds with aortic valve closing (AVC) of either derivative.

FIG. 6 shows a dZ/dt waveform where points B and X are notdistinguishable, and where point C (dZ/dt_(max)) is aligned in time withdP/dt_(max(radial)).

FIG. 7 shows placement of the electrodes on a patient implementing thetransthoracic approach, which, as described herein, is required forcalibration of the transbrachial approach if auto-calibration is notemployed. As shown, A.C. (I) is injected through a segment of the thorax(chest) between the base of the neck (laterally) 210 and lower thorax(laterally) 212 at the level of the xiphoid process (inferior portion ofthe sternum, or breast bone) in the mid-axillary line. As operationallyimplemented, an A.C. field is applied to the thoracic volume betweenpoints 214 and 216, forcing an A.C. of high frequency (50-100 kH) andlow magnitude (1.0-4.0 mA (rms)) to flow longitudinally between the neckand lower thorax. The A.C. causes, in the direction of the electricalfield, and between the current injecting electrodes, a measured voltage,U(t). U(t) is further comprised of a static D.C. component, U₀, and adynamic A.C. component, ΔU(t). The voltage, U₀, and voltage drop, ΔU(t),are sensed by electrodes proximate the current injecting electrodes, andwithin the current field. An A.C. generator 218 and voltmeter 220 areshown.

FIG. 8 shows waveform examples of the following: ECG, ΔZ(t), dZ/dt, andd²Z/dt² (Ω/s³) from the transthoracic approach. Fiducial landmarks notedon the dZ/dt waveform are point B, denoting aortic valve opening, pointC, denoting dZ/dt_(max), and point X, denoting aortic valve closure.Fiducial landmarks noted on the d²Z/dt² waveform are point B-1indicating d²Z/dt² _(max) and corresponding proximate in time to aorticvalve opening; point C-1 corresponding to the first zero crossing andthus dZ/dt_(max); and point X-1, corresponding to the second zerocrossing and aortic valve closure (point X on the dZ/dt waveform). Themagnitude, d²Z/dt² _(max), is noted.

DESCRIPTION OF PREFERRED EMBODIMENTS

The invention and the various features and advantageous details thereofare explained more fully with reference to the nonlimiting embodimentsthat are illustrated in the accompanying drawings and detailed in thefollowing description. Descriptions of well known starting materials,processing techniques, components, and equipment are omitted so as notto unnecessarily obscure the invention in detail. It should beunderstood, however, that the detailed description and the specificexamples, while indicating preferred embodiments of the invention, aregiven by way of illustration only and not by way of limitation. Varioussubstitutions, modifications, additions and/or rearrangements within thespirit and/or scope of the underlying inventive concept will becomeapparent to those skilled in the art from this disclosure.

As used herein, the terms “comprises,” “comprising,” “includes,”“including,” “has,” “having” or any other variation thereof, areintended to cover a non-exclusive inclusion. For example, a process,method, article, or apparatus that comprises a list of elements is notnecessarily limited to only those elements but may include otherelements not expressly listed or inherent to such process, method,article, or apparatus. Further, unless expressly stated to the contrary,“or” refers to an inclusive or and not to an exclusive or. For example,a condition A or B is satisfied by any one of the following: A is true(or present) and B is false (or not present), A is false (or notpresent) and B is true (or present), and both A and B are true (orpresent).

Also, use of the “a” or “an” are employed to describe elements andcomponents of the invention. This is done merely for convenience and togive a general sense of the invention. This description should be readto include one or at least one and the singular also includes the pluralunless it is obvious that it is meant otherwise.

Unless otherwise defined, all technical and scientific terms used hereinhave the same meaning as commonly understood by one of ordinary skill inthe art to which this invention belongs. Although methods and materialssimilar or equivalent to those described herein can be used in thepractice or testing of the present invention, suitable methods andmaterials are described below. All publications, patent applications,patents, and other references mentioned herein are incorporated byreference in their entirety. In case of conflict, the presentspecification, including definitions, will control. In addition, thematerials, methods, and examples are illustrative only and not intendedto be limiting.

The present invention discloses a method and apparatus for thedetermination of stroke volume (SV) and cardiac output (CO) bytransbrachial electrical bioimpedance, wherein the signal source is thebrachial artery. SV and CO, while not sensitive indices of the overallintrinsic force generation capacity, or contractility of the heartmuscle, are the best indicators of the overall performance of the heartconsidered as a muscular pump. The apparatus and method disclosedinvolve the application of a constant magnitude alternating current ofhigh frequency and small amplitude across a segment of a person's upperextremity, and more specifically, the upper arm, otherwise known as thebrachium. The present invention may also provide for calibrating thetransbrachial method and apparatus by determining SV/CO from thetransthoracic approach. Thus, in contradistinction to the generallyaccepted transthoracic bioimpedance method for SV/CO determination, thepresent invention relates to the acquisition and signal processing ofthe cardiogenically-induced, pulsatile transbrachial bioimpedance signalfor the purpose of SV/CO determination.

Advantages of the transbrachial method include:

-   -   1. Stroke volume (SV) and cardiac output (CO) values are not        affected by excess, extra-vascular, intrathoracic liquids;        namely, pulmonary edema fluid.

2. Baseline transbrachial quasi-static impedance, Z₀, is not affected bypulmonary (lung) ventilation, thereby obviating the necessity forsophisticated stabilizing adaptive filtering techniques to obtain asteady baseline for measurement of the cardiac-induced transbrachialimpedance change, ΔZ(t), and the magnitudes and fiducial landmarks onits first time-derivative, transbrachial dZ/dt and on its secondtime-derivative, d²Z/dt².

-   -   3. The cumbersome and user-unfriendly transthoracic band, or        tetrapolar spot-electrode array, is replaced by a        circumferential or non-circumferential arm band or bands, an        adhesive strip or other appropriate means for positioning the        electrodes near the brachial artery containing a bipolar, or        alternatively, a tetrapolar spot (or band) electrode array        positioned on the medial aspect of the brachium between the        axilla (arm pit) and a point distal on the brachium at the level        of the olecranon process (elbow).    -   4. With the arm at rest, motion artifacts are minimized as        compared to the transthoracic approach, and thus, adaptive        filtering techniques are less critical.    -   5. Long-term monitoring of SV/CO in the surgical operating room,        or intensive care unit, is facilitated by application of the        apparatus to the arm, containing the bipolar, or, alternatively,        the tetrapolar montage.    -   6. The bioimpedance signal obtained from the brachium is        unaffected by the presence of chest thoracostomy tubes, external        pacemaker wires, surgical bandages or appliances, and        percutaneously placed central venous access catheters located in        the neck or upper chest.    -   7. Without the perturbing influence of pulmonary ventilation,        and pulmonary artery and other intrathoracic large vessel venous        pulsations, the signal to noise ratio (S/N) relating to those        portions the transbrachial dZ/dt and d²Z/dt² signals pertaining        only to left ventricular ejection are substantially higher than        that of the transthoracic approach.

As disclosed above, the present invention relates to the measurement ofstroke volume (SV) and cardiac output (CO) from the transbrachialmethod, using the brachial artery as the cardiogenically-induced signalsource. Methodologically, the transbrachial method is similar to thetransthoracic technique for determining SV. However, in thetransthoracic technique, signal acquisition is effected over a segmentof thorax by placement of voltage sensing electrodes 214 at the base ofthe neck, bilaterally, and voltage sensing electrodes 216 at the lowerthorax at the xiphoid level, bilaterally (see FIG. 7). In contrast, thetransbrachial technique uses a segment of brachium between voltagesensing electrodes 112/114 positioned proximate the axilla (arm pit) andjunction of the upper and lower arm at the level of the olecranonprocess of the elbow. (see FIG. 1).

FIG. 1 schematically shows one apparatus embodiment according to thepresent invention, and its electrical interface with a subject 100.Signal acquisition from the upper arm 102 (brachium) requiresapplication of a constant magnitude alternating current (A.C.) 104 ofhigh frequency and small amplitude to electrodes 106, 108 that arespaced apart, with one or more electrodes affixed to the skin of theaxilla, as well as one or more electrodes placed medially at the levelof the antecubital fossa creating a current field. In this embodiment,the electrodes are applied to the subject's left arm. In otherembodiments, the electrodes may be positioned on the right arm.

With the current field thus generated, the potential difference betweenthe current injecting electrodes or alternating current flow electrodes106, 108 is measured by a voltmeter 110 connected to the voltage sensingelectrodes 112, 114 placed within the current field (see FIG. 1). Abaseline impedance between the voltage sensing electrodes 112, 114, aswell as a change in impedance, ΔZ(t) can be measured transbrachially.When the ΔZ(t) signal is electronically differentiated,dZ/dt_((brachium)) results, its peak systolic magnitude beingdZ/dt_(max(brachium)). For the purposes of the invention disclosedherein, dZ/dt_(max) (Ω/s²) is equivalent to the nadir, or peak negativevalue of the rate of change of the impedance variation, dZ/dt_(min). Itis also understood and stipulated that−dZ/dt_(max)=+dZ/dt_(max)=dZ/dt_(min). When dZ/dt undergoes electronicdifferentiation, d²Z/dt²(brachium) (Ω/s³) results, its peak magnitudebeing d²Z/dt² _(max(brachium)). For the purposes of the inventiondisclosed herein, d²Z/dt² and d²Z/dt² _(max) are equivalent to the rateof change and peak negative rate of change of dZ/dt and dZ/dt_(min),respectively. In the context of dZ/dt_(max) being equivalent todZ/dt_(min), the interpretation of the peak magnitudes of theirrespective derivatives should be understood and furthermore stipulatedas equivalent (d²Z/dt² _(max)=d²Z/dt² _(min)). Many different methods ofapplying the electrodes or electrode arrays to the arm are envisioned,such as spot electrodes, arm band(s) both circumferential andnon-circumferential, adhesive strips or other attachment means known inthe art. In one embodiment, an 8 spot-electrode array can beimplemented. Alternatively, in another embodiment, a 4 spot-electrodearray, placed on the inner, or medial aspect of the upper arm, proximatethe brachial artery, can be implemented. Alternatively, 4non-circumferential band (strip) electrodes, embedded in an adhesivecarrier, may be affixed to the brachium, medially, and used in lieu ofspot electrodes.

The voltages measured by the Voltmeter 110 not only contains a signalcaused by the AC applied, but may also contain a signal component fromwhich an electrocardiogram (ECG) can be derived. The application offilters separates the AC related and ECG related signal components. Inanother embodiment, EKG 116 may also be measured by placing EKGelectrodes 118 on the patient 100. In the figure, a 3-lead EKG is shownand EKG is measured by known means. The magnitude of the alternatingcurrent (A.C.) 104 and voltmeter 110 may be components of an apparatus120. The apparatus 120 may also include an input device and a processor.The input device may be any suitable device that provides information tothe apparatus, such as a keyboard. The input device may also receiveinformation from external sources, such as the EKG 116. The processor isin communication with the data input device, the alternating currentsource 104 and electrodes 106, 108, and the voltmeter 110 and electrodes112, 114. The processor is capable of receiving the information andcalculating the stroke volume and cardiac output of the patient 100. Thestroke volume and cardiac output of the patient may be displayed on ascreen or be sent to other devices via a data output device of theapparatus.

FIG. 2 shows an example of ECG, ΔZ(t) and dZ/dt waveforms from a humansubject 100, where T_(RR)=the R-R interval, or the time for one cardiaccycle; Q=onset of ventricular depolarization; ---------=maximum systolicupslope extrapolation of ΔZ(t); B=aortic valve opening; C=peak rate ofchange of the thoracic cardiogenic impedance variation, dZ/dt_(max);X=aortic valve closure; Y=pulmonic valve closure; O=rapid ventricularfilling wave; Q-B interval=pre-ejection period, T_(PE); B-Cinterval=time-to-peak dZ/dt, TTP; B-X interval=left ventricular ejectionperiod, T_(LVE). dZ/dt waveform to the right shows dZ/dt_(max) remainingconstant throughout the ejection interval, T_(LVE).

Rationale for use of the brachium as an appropriate anatomic site for SVmeasurement by the bioimpedance technique is as follows. When A.C. (I)is injected through a segment of upper arm, otherwise known as thebrachium, the boundaries of which are the deltoid muscles of theshoulder and axilla, proximally, and the elbow and antecubital fossa,distally, a quasi-static voltage, U₀, and voltage change, ΔU(t), can bemeasured between the current injecting electrodes. Embedded within thebrachial musculature and connective tissue, and anatomically situatedmedial to the brachial bone, otherwise known as the humerus, is thebrachial artery. The brachial artery is a large artery, continuous withboth the subclavian and axillary arteries, and, whereas the leftsubclavian artery is a major branch of the arch of the thoracic aorta,the right subclavian artery is a branch of the brachiocephalic artery.The contents of the upper arm, including connective tissue, bone,nervous tissue, veins, and the brachial artery, comprise an impedance(Z) to current flow. The passage of A.C. across the brachium generates aquasi-static voltage, U₀, and, concordant with every pressure pulse ofthe brachial artery, a time-dependent drop in measured transbrachialvoltage, ΔU(t), this following shortly after the onset of leftventricular ejection. The magnitude of the time delay (Δt, ms) betweenthe brachial artery pressure pulse and the onset of left ventricularejection is a function of pulse wave velocity. Transthoracically, thepeak rate of change of impedance, dZ/dt_(max), resulting from electronicdifferentiation of ΔZ(t), corresponds in time with peak aortic bloodacceleration, dv/dt_(max) (cm/s²). Thus, in the preferred embodiment ofthe invention, dZ/dt_(max(brachial)) represents the ohmic analog of peakblood acceleration in the brachial artery. Chemla et al. (Fundam ClinPharmacol 1996; 10:393-399) showed that the measured acceleration ofblood in the brachial artery is highly correlated (r=0.79) and linearlyproportional with blood acceleration in the ascending aorta. Moreover,whereas the magnitude of brachial artery blood velocity is affected bydownstream peripheral vasoactivity (vasodilation, vasoconstriction), themagnitude of brachial artery blood acceleration is modulated only bybeta (β) adrenergic stimulation or depression of the cardiacadrenoceptors (Chemla D, et al. Am J Cardiol 1990; 65:494-500). Asextrapolated from Visser (Ann Biomed Eng 1989; 17:463-463), when flowingblood is interrogated by a field of alternating current (A.C.), theacceleration of blood in the aorta is measured as the aortic reducedaverage blood acceleration which is the mean aortic acceleration dividedby the vessel radius: (dv/dt_((mean))/R). When[(dv/dt_((mean))/R]_(max), or peak aortic reduced average bloodacceleration (1/s²), undergoes square root transformation, peak aorticreduced average blood velocity (1/s) results. Likewise, whendZ/dt_(max)/Z₀ (1/s²) undergoes square root transformation, ohmic meanvelocity results, ΔZ_(v)(t)_(max)/Z₀ (1/s). In the context of thepresent invention, where dZ/dt_(max) represents ohmic mean acceleration,dZ/dt_(max)/Z₀ is herein referred to as the acceleration index (ACI).Because of the high correlation of dv/dt_(max) measured in the aorta,with that of the brachial artery, it is claimed by the present inventionthat SV can also be obtained from the brachial artery. It has beendiscovered that processing the mean value of the second time-derivativeof the impedance change provides results equivalent to processing thepeak value of the first time-derivative, but with better accuracy. Thus,in the preferred embodiment, $\begin{matrix}{{SV}_{TB} = {V_{C} \cdot \sqrt[3]{\lbrack {( \frac{{\mathbb{d}^{2}Z}/{\mathbb{d}t_{mean}^{2}}}{Z_{0}} ) \cdot 10^{- 2}} \rbrack} \cdot T_{LVE}}} & {{equation}\quad 1}\end{matrix}$where SV_(TB)=transbrachial SV (mL); V_(c(brachium)) equals the volumeconductor (mL); Z₀ equals the quasi-static transbrachial base impedance(Ohm, Ω); T_(lve) equals left ventricular ejection time (s), and d²Z/dt²_(mean) equals the mean value of the second time-derivative of thecardiogenically induced transbrachial impedance variation (Ω/s³). In afirst embodiment:d ² Z/dt ² _(mean)=(dZ/dt _(max))/TTP _(m),  equation 1awhere TTP_(m)=measured time to peak dZ/dt, defined as the temporalinterval from point B to point C (seconds, s) in FIG. 2. In a secondembodiment:d ² Z/dt ² _(mean)=(dZ/dt _(max))/TTP _(m),  equation 1bwhere 0.01 s≦TTP≦0.1 s, such as TTP_(b)=0.06 s. In a third embodiment:d ² Z/dt ² _(mean)=(dZ/dt _(max))/TTP _(c),  equation 1cwhere TTP_(c)=corrected rise time, or time to peak dZ/dt, which is thecorrected temporal interval from point B to point C (s). Here,TTP_(c)=(10^(−a))×[1/(ACI)^(b)=s; where [1/(ACI)^(b)]=ACI^(b); “a” is anegative exponent such as 0>a≧5 or even a=−2; ACI=accelerationindex=dZ/dt_(max)/Z₀=1/s²; “b” is an exponent such as 0.1≦−b≦1.0 or evenb=0.5; where −b (minus b) is a negative exponent such as 0>−b≧10 or even−b (minus b)=−0.5; and 0.01 s≦TTP_(c)≦0.1 s. For example, in a preferredembodiment, TTP_(c)=(10⁻²)×[1/(ACI)^(0.5)]=s. In a fourth embodiment:d ² Z/dt ² _(mean) =dZ/dt _(max) /TTP _(d),  equation 1dwhere TTP_(d)(s)=(TTP_(c)+TTP_(m))/A; and 0<A≦5 such as A=2; and 0.01s≦TTP_(d)≦0.1 s. In a fifth embodiment:d ² Z/dt ² _(mean) =dZ/dt _(max) /TTP _(e),  equation 1ewhere TTP_(c)(s)=(TTP_(c)+TTP_(b))/A; and 0<A≦5 such as A=2; and 0.01s≦TTP_(c)≦0.1 s. In a sixth embodiment:d ² Z/dt ² _(mean) =dZ/dt _(max) /TTP _(f),  equation 1fwhere TTP_(f)=(TTP_(m)+TTP_(b))/A; and 0<A≦5 such as A=2; and 0.01s≦TTP_(f)≦0.1 s. In a seventh embodiment:d ² Z/dt ² _(mean) =d ² Z/dt ² _(max) /B;  equation 1gwhere d²Z/dt² _(max) (Ω/s³)=the maximal systolic upslope extrapolationof dZ/dt, peak first time-derivative of dZ/dt, or systolic peak rate ofchange of dZ/dt; and 0<B≦10 such as B=2.

In one exemplary embodiment:

-   -   V_(c(brachium))=C₁·[W·C₂];    -   C₁=0<C₁≦50,000,    -   W=weight in kilograms (kg)    -   C₂=C₃/(BMI_(n))^(y)    -   BMI_(n)=BMI_(p)/C₄        -   a. 35≦C₃≦100 (mL/kg), wherein C₃ in the preferred            embodiment=70 mL/kg;        -   b. BMI_(n)=normalized body mass index (dimensionless),            wherein 0.5≦BMI_(n)≦1.0, wherein the preferred embodiment,            BMI_(n)=1        -   c. BMI_(p)=a person's body mass index=Weight (kg)/Height            (meters)² (kg/m²) where W=a person's weight (kg), and H=a            person's height (m).        -   d. 15≦C₄≦40 kg/m², wherein C₄=ideal body mass index=24 kg/m²            in the preferred embodiment.        -   e. 0.25≦y≦1.0, wherein y=0.5 in the preferred embodiment.        -   f. 35≦C₂≦100, wherein the preferred embodiment, C₂=70 mL/kg

Unlike previously described bioimpedance techniques, which broadlyassume a plethysmographic or volumetric origin for the cardiogenicimpedance change, ΔZ(t), and its peak first time derivative,dZ(t)/dt_(max), the present technique assumes dZ(t)/dt_(max) torepresent the ohmic equivalent of the peak acceleration of red bloodcells. Thus, when the first time-derivative of ΔZ(t) is taken, dZ/dt,its peak magnitude, dZ/dt_(max), can be shown to coincide in time withthe peak red blood cell acceleration, dv/dt_(max) (cm/s²), and not withthe peak rate of change of volume, dV/dt_(max) (mL/s). Consequently, toobtain ohmic mean velocity, dZ/dt_(max)/Z₀ (1/s²) must undergo squareroot transformation. This transformation is to be known as square rootAcceleration Step-down Transformation: √{square root over([)}(dZ/dt_(max))/Z₀] (1/s). It can also be shown that the cube root ofthe normalized mean value of the second time-derivative of the impedancechange times 10⁻², that is, [(d²Z/dt² _(mean)/Z₀)×10⁻²]^(0.333), yieldsohmic mean velocity equivalent to the taking the square root of the peakvalue of the first time-derivative. Signal processing the mean value ofthe second time-derivative of ΔZ(t) has certain advantages overprocessing the first time-derivative (e.g. time to peak valuescalculated more accurately because of using cube root calculations oversquare root calculations), which are provided in another preferredembodiment using the transthoracic approach. To obtain brachial arteryohmic mean velocity, the cube root transformation is thus implemented inthe preferred embodiment. Thus, the signal processing technique,comprising part of the invention, implies that the proper designationfor the transbrachial approach is correctly stated as TransbrachialElectrical Bioimpedance Cardiovelocimetry or, simply, Transbrachialbioimpedance velocimetry.

Impedance Measurement Techniques in the Preferred Embodiment of theInvention

FIGS. 3 a and 3 b show the relationship between the dZ/dt curve andeither the dP/dt or d(SpO₂)/dt curves. FIG. 3 a further shows an examplewhere points B and X are apparent on the dZ/dt curve and FIG. 3 b showsan example where point B is not detectable, but point X is detectable onthe dZ/dt curve. Thus, determination of left ventricular ejection time,(T_(lve)), onset of flow (point B), and the ohmic equivalent of peakbrachial artery reduced average blood acceleration,(dZ/dt_(max)/Z_(0 (brachium))), while ideally measured directly from thedZ/dt curve, are supplemented obligatorily by alternative means. Thesaid alternative/obligatory means for determining T_(lve) are thoseobtained from means such as from the waveform corresponding to thephotoplethysmographic pulse oximetry waveform, ΔSpO₂(t), or its firsttime-derivative, d(SpO₂)/dt, and/or by the waveform obtained from anon-invasive applanated radial arterial pressure pulse waveform,ΔP(t)(radial), or its first time-derivative, dP/dt_((radial)). (see FIG.4)

The said means for determining point B on the transbrachial dZ/dt curveare those methods used for determining T_(lve) when point X on thetransbrachial dZ/dt curve, or its first time derivative (d²Z/dt²), areidentifiable by those skilled in the art of bioimpedance curve analysis.When point X is not identifiable on the transbrachial dZ/dt curve, orits first time-derivative, d²Z/dt², then alternative means for point Bdetection are necessary. In the absence of an identifiable point X bythose skilled in the art of dZ/dt curve analysis, said means for point Bdetection include use of the first time-derivative of the applanatedradial pressure waveform tracing, dP/dt_((radial)). It will be clear tothose skilled in the art of curve analysis, why the aforementioned saidmeans are superior to those disclosed by others, and most recently byBaura et al. (U.S. Pat. No. 6,561,986 B2).

Methods for Determination of Left Ventricular Ejection Time (T_(lve),LVET):

-   -   1. dZ/dt waveform analysis: T_(lve) (LVET) measured across the        brachium is defined as the temporal interval from point B, which        corresponds to aortic valve opening (AVO), albeit with a time        delay, to point X, which coincides in time, albeit with a short        time delay, to aortic valve closure (AVC), these time delays        dictated by pulse wave velocity.    -   2. d²Z/dt² waveform analysis: T_(LVE) (LVET) measured from the        peak second time-derivative of the transbrachial or        transthoracic impedance pulse variation is defined as the        temporal interval proximate the peak of the earliest positive        systolic deflection of d²Z/dt² (i.e. d²Z/dt² _(max)),        corresponding proximate in time with point B on the dZ/dt curve        and the nadir of the rising foot of ΔZ(t), to, in the usual        case, the second zero baseline impedance crossing of d²Z/dt². To        the ejection interval just described, 20 ms (i.e. 0.02 seconds)        should be added. The second Zero crossing, following the first        zero crossing corresponding to point C (dZ/dt_(max)),        corresponds temporally with point X on the dZ/dt curve. These        relationships are better appreciated by inspection of FIG. 8.    -   3. Pulse Oximetry waveform (ΔSpO₂(t)): LVET is defined as the        temporal interval (seconds) from the onset of the oximetric        pulse at zero baseline, signifying the onset of ejection, albeit        with a time delay, to the oximetry wave equivalent of the        dicrotic notch, which signifies aortic valve closure, albeit        with a time delay, and the end of ejection. The oximetry        waveform can be obtained from any appropriate site on, or within        the human body, but, in the preferred embodiment, the distal        digit of the human finger is deemed most appropriate.    -   4. Applanation Tonometry Pressure Pulse waveform        (ΔP(t)_((radial))): LVET is defined as the temporal interval        (seconds) from the onset of the pressure pulse at zero baseline,        signifying the onset of ejection, albeit with a time delay, to        the dicrotic notch equivalent, which signifies aortic valve        closure, albeit with a time delay, and the end of ejection. In        the preferred embodiment, the pressure pulse waveform is        obtained from the radial artery at the wrist, but may be        obtained from any site on the arm, specifically from either        brachial artery.    -   5. Regression Equations for T_(lve) versus Heart Rate (HR): LVET        is determined by Weissler's regression equations: Male:        T_(lve)=−0.0017·HR+0.413; Female: T_(lve)=−0.0016·HR+0.418.        It should be noted that any of the above methods of LVET        determinations can be used solely, or in combination with each        other (e.g. average multiple LVET determinations, use one or        more determinations that appear to produce better results,        etc.).

With exemplary dZ/dt waveforms, such as those shown in FIG. 3 a, point Band point X are readily distinguishable by one skilled in the art ofcurve analysis. However, these fiducial landmarks are frequentlydistorted by motion and ventilation artifacts (especially using thetransthoracic approach), as well as by certain disease processes. LVETmay be more accurately measured by curve analysis of the pulse oximetryand applanation tonometry waveforms (FIG. 3 b), or their firsttime-derivatives. In one embodiment of the invention, either or bothmethods may be implemented. Of these techniques, applanation tonometryis most likely to demonstrate a dicrotic notch, and, therefore, isconsidered the preferred technique. Furthermore, for those skilled inthe art of computer waveform analysis, the points coinciding with thebeginning and end of ejection can be readily identified from the firsttime-derivative curves of both the oximetry and applanation tonometrywaveforms; namely, d(SpO₂)/dt and dP/dt_((radial)). In the preferredembodiment, the best method constitutes computer analysis of the firsttime-derivatives. In another embodiment, regression equations for heartrate versus LVET may be implemented.

Methods for Point B Detection on the dZ/dt Waveform:

-   -   1. Methods for determining point B when point X is readily        identifiable by one skilled in the art of curve analysis (see        FIG. 3 a).

Point B on the transbrachial dZ/dt waveform is known to coincide withaortic valve opening, albeit with a time delay. Exemplary dZ/dtwaveforms demonstrate a distinct change in slope at, or not uncommonlyabove the zero baseline impedance, followed by a steep, positive linearsegment ending at point C, or dZ/dt_(max). When a distinct change inslope leading to point C is detected at or above the baseline, oneskilled in the art of curve analysis can readily identify point B.However, as demonstrated by Debski T T et al. (Biol Psychol 1993;36:63-74) using the transthoracic method, despite using fiduciallandmarks on the time-derivatives of dZ/dt (i.e. d²Z/dt² and d³Z/dt³) toidentify this change in slope, detection of point B can be problematic.This inability to correctly identify point B is obvious to those skilledin the art of curve analysis, and especially curve analysis of dZ/dt, byinspection of FIG. 3 b. The method disclosed herein provides a new andinnovative solution for point B detection. The new method employs one,or a combination of methods disclosed under determination of LVET;namely, ΔSpO₂(t) and/or ΔP(t)_((radial)) (as shown in FIG. 4), or,respectively, their time derivatives, d(SpO₂)/dt and/or dP/dt_((radial))(as shown in FIG. 5). The technique of point B detection, as disclosedherein as a preferred embodiment, involves computerized curve fittingand alignment in time of temporal landmark X on the transbrachial dZ/dtcurve with the dicrotic notch equivalent of one or both of the measuredaforementioned oximetry and pressure curves, and/or preferably with oneor both of their first time-derivatives. Independently, or in concert,one or both of the first time-derivative curves can be aligned in timewith the transbrachial dZ/dt curve, such that the temporal point of thetermination of flow, or aortic valve closure (AVC) equivalent on thefirst derivative oximetry or pressure curves, can be aligned in timewith point X of the transbrachial dZ/dt curve. Point B, coinciding withaortic valve opening (AVO), and the beginning of flow, albeit with atime delay, is identified by determining the temporal point on thetransbrachial dZ/dt curve, intersecting, and coinciding in time with thepoint of onset of flow/pressure on the ΔSpO₂(t)/AP(t) curves, and/or ontheir first time-derivatives. This temporal point is identified as adiscreet point at the baseline occurring before the first positivemaximum upslope measured from foot of the respective baselines of theΔSpO₂(t) and/or ΔP(t)_((radial)) curves, and/or from their firsttime-derivatives (FIGS. 3 a, 3 b, 4, 5, 6).

-   -   2. Method for determining point B when point X is not readily        identifiable by one skilled in the art of curve analysis (see        FIG. 6):

When point X is not readily identifiable by one skilled in the art ofcurve analysis, then alternative means must be applied. Requiringalternative means, for example, would be the inability to identify thefirst zero crossing at baseline impedance after the zero crossing ofpoint C (dZ/dt_(max)) on the second time-derivative curve of ΔZ(t)(i.e.,d²Z/dt²), where said zero crossing corresponds in time to point X andAVC. Said alternative means requires application of the firsttime-derivative of the applanation tonometry curve, dP/dt_((radial))(FIG. 6). For one skilled in the art of curve analysis, said meansrequires alignment in time of the earliest maximum positive peak ofdP/dt (dP/dt_(max)) with point C of the transbrachial dZ/dt curve. Withpoint dP/dt_(max) and point C aligned in time, point B can be identifiedby applying a perpendicular through, and coinciding in time with theonset at baseline of the first positive deflection of dP/dt, where saidperpendicular line must intersect the dZ/dt curve at or above baselineimpedance. The point of intersection of the perpendicular with thetransbrachial dZ/dt curve is designated point B. When the above methodsare unavailable, or fail to supply waveforms with fiducial landmarksnecessary for point B detection, as assessed by pre-determined criteria,then, as default methods, a point on the transbrachial dZ/dt curveoccurring 55 ms prior to point C, but obligatorily at or above baselineimpedance, or alternatively, a point 15% above baseline impedance on thedZ/dt curve, is taken as point B.

Method for determining the maximum systolic upslope of transbrachialdZ/dt, otherwise known as transbrachial d²Z/dt² _(max): Employing one ora combination of the techniques described herein for point B detection,transbrachial d²Z/dt² _(max) is the measured peak positive deflection ofthe d²Z/dt² (d²Z/dt² _(max)) curve usually occurring temporallyproximate point B on the transbrachial dZ/dt curve.

In one embodiment, external calibration of the SV/CO by means of thetransbrachial approach:

-   -   1. External calibration of V_(c(brachium)) by means of the        transthoracic method: Determination of V_(c(cal)).

Because of the high correlation of dv/dt_(max) measured in the aortawith that of the brachial artery, it is claimed that: $\begin{matrix}\begin{matrix}{V_{C{({thorax})}} = {\sqrt[3]{\lbrack {( \frac{{\mathbb{d}^{2}Z}/{\mathbb{d}t_{mean}^{2}}}{Z_{0}} )_{thorax} \cdot 10^{- 2}} \rbrack} \cdot T_{LVE}}} \\{= {V_{C{({brachium})}} \cdot}} \\{\sqrt[3]{\lbrack {( \frac{{\mathbb{d}^{2}Z}/{\mathbb{d}t_{mean}^{2}}}{Z_{0}} )_{transbrachial} \cdot 10^{- 2}} \rbrack} \cdot T_{LVE}}\end{matrix} & ( {{equation}\quad 2} )\end{matrix}$

Since T_(lve) is equivalent for both sides of equation 2,V_(c(brachium)) can be found thusly, $\begin{matrix}\begin{matrix}{V_{C{({cal})}} = V_{C{({brachium})}}} \\{= \frac{V_{C{({thorax})}}\sqrt[3]{\lbrack {( \frac{{\mathbb{d}^{2}Z}/{\mathbb{d}t_{mean}^{2}}}{Z_{0}} )_{thorax} \cdot 10^{- 2}} \rbrack}}{\sqrt[3]{\lbrack {( \frac{{\mathbb{d}^{2}Z}/{\mathbb{d}t_{mean}^{2}}}{Z_{0}} )_{transbrachial} \cdot 10^{- 2}} \rbrack}}}\end{matrix} & {{equation}\quad 3} \\{{{Where}\quad V_{c{({thorax})}}} = {C_{1{({thorax})}} \cdot \lbrack {{W({kg})} \cdot C_{2}} \rbrack}} & {{equation}\quad 4}\end{matrix}$Where 0.10≦C_(1(thorax))≦0.75, wherein C₁=0.25 in the preferredembodiment,

Thus, SV by the transbrachial method, externally calibrated from thetransthoracic approach is given as, $\begin{matrix}{{SV}_{transbrachial} = {V_{C{({cal})}} \cdot \sqrt[3]{\lbrack {( \frac{{\mathbb{d}^{2}Z}/{\mathbb{d}t_{mean}^{2}}}{Z_{0}} )_{transbrachial} \cdot 10^{- 2}} \rbrack} \cdot T_{LVE}}} & {{equation}\quad 5}\end{matrix}$

2. Determination of SV from the transbrachial approach by means ofauto-calibration: A priori determination of C_(1(brachium)) as a meanvalue for a population, n.

In order to satisfy the requirements of equation 2, V_(c(brachium)) isfound by determining V_(c(cal)) from the solution of equation 3. Thisoperation requires insertion of V_(c(thorax)) as determined fromequation 4. Therefore, V_(c(cal)) in equation 3 can be determinedthusly;V _(c(cal)) =C _(1(brachium)) ·[W(kg)·C ₂]  equation 6Where, C₁ is thus,C _(1(brachium)) =V _(c(cal)) /[W(kg)·C ₂]  equation 7where, 0≦C₁≦50,000, wherein the preferred embodiment C₁ is proprietary.

By solving equation 7 for a population, n, determining V_(c(cal)) fromequation 3, the mean value of the constant, C_(1(brachium)), can befound for the general population as follows;C _(1(brachium))(mean)=[(C ₁₋₁ +C ₁₋₂+C₁₋₄+ . . . C_(1-n))/n]  equation8Where C_(1(mean)) ideally=C₁₋₁ through C_(1-n). Thus, SV determinationby the transbrachial approach by auto-calibration is given as,$\begin{matrix}{{SV}_{transbrachial} = {\lbrack {C_{1{({{mean},{brachial}})}} \cdot W \cdot C_{2}} \rbrack \cdot \sqrt[3]{\lbrack {( \frac{{\mathbb{d}^{2}Z}/{\mathbb{d}t_{mean}^{2}}}{Z_{0}} )_{transbrachial} \cdot 10^{- 2}} \rbrack} \cdot T_{LVE}}} & {{equation}\quad 9}\end{matrix}$

In another embodiment of the present invention, the SV of the leftventricle can be determined using the transthoracic approach and themean value of the second time-derivative of the cardiogenically inducedtransthoracic impedance variation (Ω/s³). As implemented by inspectionof FIG. 7 and related description, a tetrapolar spot electrode array canbe applied to a person's body. The description of signal acquisition andprocessing is precisely that described above with respect to FIG. 2.Stroke volume determination by means of the transthoracic (TT)application is implemented by means of the following equation (where, inthe general embodiment, the stroke volume (SV) equation is given as):$\begin{matrix}{{SV}_{TT} = {V_{C{({TT})}} \cdot \sqrt[3]{\lbrack {( \frac{{\mathbb{d}^{2}Z}/{\mathbb{d}t_{mean}^{2}}}{Z_{0}} )_{TT} \cdot 10^{- 2}} \rbrack} \cdot T_{LVE}}} & {{equation}\quad 10}\end{matrix}$Where:

-   -   SV_((TT))=stroke volume by the transthoracic approach (mL).    -   V_(C(TT))=Volume conductor (mL), otherwise known as the volume        of electrically participating thoracic tissue (V_(EPT)).        $\begin{matrix}        {{{Ohmic}\quad{mean}\quad{velocity}\quad( {1\text{/}\sec} )} = \sqrt[3]{\lbrack {( \frac{{\mathbb{d}^{2}Z}/{\mathbb{d}t_{mean}^{2}}}{Z_{0}} )_{TT} \cdot 10^{- 2}} \rbrack}} & {{equation}\quad 11}        \end{matrix}$

d²Z/dt² _(mean) is determined identically as described above with regardto equations 1 and 1a-1g.

T_(LVE)=left ventricular ejection time (seconds, sec, s).

Evaluation, ranges and preferred embodiments of the input variables ofequation 10 are as follows: $\begin{matrix}{{V_{C{({TT})}} = {\zeta \cdot ( {C_{2} \cdot W \cdot C_{3}} )}}{{\zeta\quad({zeta})} = {( {C_{1} - {C_{1}\frac{Z_{0}}{Z_{c}}} + \frac{Z_{0}^{2}}{Z_{c}^{2}}} )\quad({dimensionless})}}} & {{equation}\quad 12}\end{matrix}$

-   -   1.0≦C₁≦8.0, wherein the preferred embodiment C₁=4.    -   Z₀ (Ohm, Ω)=the transthoracic base impedance, or static D.C.        component of the total transthoracic impedance, Z(t).    -   Z_(c) (Ω)=the critical level of base impedance; wherein, 15        Ω≦Z_(c)≦25 Ω, and wherein the preferred embodiment, Z_(c)=20 Ω.        For all values of Z₀<20 Ω, ζ>1.0, and for all values of Z₀<20 Ω,        ζ=1.0.    -   0.10≦C₂≦0.75, wherein the preferred embodiment, C₂=0.25    -   W=weight in kilograms (kg) $\begin{matrix}        {C_{3} = {\frac{C_{4}}{( {BMI}_{N} )^{y}} = {{mL}\text{/}{kg}}}} & {{equation}\quad 13}        \end{matrix}$    -   35≦C₄≦100=mL/kg, wherein the preferred embodiment, C₄=70 mL/kg.    -   BMI_(N)=normalized body mass index (dimensionless), where        0.5≦BMI_(N)≦5.0, wherein the preferred embodiment BMI_(N)=1.0.    -   BMI_(N)=BMI_(p)/C₅

BMI_(P)=a person's body mass index (W(kg)/H(m²), i.e. kg/m²), where W=aperson's weight in kilograms (kg), and H=a person's height in meters(m).

-   -   C₅=a person's ideal body mass index (kg/m²), where 10≦C₅≦100,        wherein the preferred embodiment, C₅=24 kg/m².    -   y is an exponent, 0.25≦y≦1.0, wherein the preferred embodiment,        y=0.5, where 1/y=equivalent root function, where, ^(1/y)√{square        root over (BMI_(N))}=(BMI_(N))^(y).    -   35≦C₃≦100, wherein the preferred embodiment, C₃=70 mL/kg.        $\begin{matrix}        {{V_{C{({TT})}}\quad({mL})} = \lbrack {( {C_{1} - {C_{1}\frac{Z_{0}}{Z_{c}}} + \frac{Z_{0}^{2}}{Z_{c}^{2}}} ) \cdot ( {C_{2} \cdot W \cdot C_{3}} )} \rbrack} & {{equation}\quad 14}        \end{matrix}$

The preferred embodiment the product of C₂ and C₃ is a constant K, (i.e.C₂·C₃=K), where 10≦C₂·C₃≦35, wherein the preferred embodiment,C₂·C₃=17.5 mL/kg

Where equation 11 in the broadest definition is given as,$\begin{matrix}\begin{matrix}{\begin{matrix}{{Ohmic}\quad{mean}} \\{{velocity}\quad( {1/\sec} )}\end{matrix} = \sqrt[n_{1}]{\lbrack {( \frac{{\mathbb{d}^{n_{2}}Z}/{\mathbb{d}t_{mean}^{n_{2}}}}{Z_{0}} )_{TT} \cdot 10^{- n_{3}}} \rbrack}} \\{= \lbrack {( \frac{{\mathbb{d}^{n_{2}}Z}/{\mathbb{d}t_{mean}^{n_{2}}}}{Z_{0}} )_{TT} \cdot 10^{- n_{3}}} \rbrack^{n_{4}}}\end{matrix} & {{equation}\quad 15}\end{matrix}$Where:

-   -   1.0≦n₁≦10, wherein the preferred embodiment, n₁=3.    -   1.0≦n₂≦10, wherein the preferred embodiment, n₂=2.    -   0<n₃≦5, wherein the preferred embodiment, n₃=2.    -   0.1≦n₄≦1.0, wherein the preferred embodiment, n₄=0.333.        $n_{4} = \frac{1}{n_{1}}$    -   T_(LVE)=left ventricular ejection time (seconds, sec).

Where the stroke volume equation for the transthoracic application inits broadest definition is given as, $\begin{matrix}{{SV}_{TT} = {\lbrack {( {C_{1} - {C_{1}\frac{Z_{0}}{Z_{c}}} + \frac{Z_{0}^{2}}{Z_{c}^{2}}} ) \cdot ( {C_{2} \cdot W \cdot C_{3}} )} \rbrack \cdot \sqrt[n_{1}]{\lbrack {( \frac{{\mathbb{d}^{n_{2}}Z}/{\mathbb{d}t_{mean}^{n_{2}}}}{Z_{0}} ) \cdot 10^{- n_{3}}} \rbrack} \cdot T_{LVE}}} & {{equation}\quad 16}\end{matrix}$Wherein as operationally implemented in the preferred embodiment, thestroke volume equation for the transthoracic application is given as,$\begin{matrix}{{SV}_{TT} = {\lbrack {( {C_{1} - {C_{1}\frac{Z_{0}}{Z_{c}}} + \frac{Z_{0}^{2}}{Z_{c}^{2}}} ) \cdot ( {C_{2} \cdot W \cdot C_{3}} )} \rbrack \cdot \sqrt[3]{\lbrack {( \frac{{\mathbb{d}^{2}Z}/{\mathbb{d}t_{mean}^{2}}}{Z_{0}} )_{TT} \cdot 10^{- 2}} \rbrack} \cdot T_{LVE}}} & {{equation}\quad 17}\end{matrix}$

It is to be understood that the present invention is not limited to theembodiment(s) described above and illustrated herein, but encompassesany and all variations falling within the scope of the appended claims.

1. An apparatus for determining stroke volume by bioimpedance from apatient, comprising: two or more spaced apart alternating current flowelectrodes positionable on a patient; two or more spaced apart voltagesensing electrodes positionable on the patient and between thealternating current flow electrodes; an alternating current sourceelectrically connected to the alternating current flow electrodes; avoltmeter electrically connected to the voltage sensing electrodes; anda processing unit in communication with the voltage sensing electrodes,wherein the processing unit is capable of using a voltage sensed by thevoltage sensing electrodes to calculate a mean value of a secondtime-derivative of a cardiogenically induced impedance variation of thepatient and to determine therefrom a stroke volume of the patient. 2.The apparatus of claim 1, wherein the alternating current flowelectrodes and the voltage sensing electrodes are positionable on an armof the patient proximate a brachial artery.
 3. The apparatus of claim 1,wherein the alternating current flow electrodes and the voltage sensingelectrodes are positionable on a base of the patient's neck and on alower thorax of the patient.
 4. The apparatus of claim 1, wherein theprocessing unit calculates the mean value of the second time-derivativeof the cardiogenically induced impedance variation as a peak rate ofchange of the cardiogenically induced impedance variation divided by atime to peak value of the cardiogenically induced impedance.
 5. Theapparatus of claim 4, wherein the time to peak value is a measured timeperiod between an aortic valve of the patient opening and a peak rate ofchange of the cardiogenically induced impedance variation.
 6. Theapparatus of claim 4, wherein the time to peak value is a selected timevalue at least as great as 0.01 seconds and no greater than 0.1 seconds.7. The apparatus of claim 4, wherein the time to peak value is acorrected rise time between an aortic valve of the patient opening and apeak rate of change of the cardiogenically induced impedance variation.8. The apparatus of claim 4, wherein the time to peak value iscalculated as (TTP_(c)+TTP_(m))/A, where TTP_(m) is a measured timeperiod between an aortic valve of the patient opening and a peak rate ofchange of the cardiogenically induced impedance variation, TTP_(c) is acorrected rise time between an aortic valve of the patient opening and apeak rate of change of the cardiogenically induced impedance variation,and A is a value greater than zero but not greater than
 5. 9. Theapparatus of claim 4, wherein the time to peak value is calculated as(TTP_(c)+TTP_(b))/A, where TTP_(b) is a selected time value at least asgreat as 0.01 seconds and no greater than 0.1 seconds, and TTP_(c) is acorrected rise time between an aortic valve of the patient opening and apeak rate of change of the cardiogenically induced impedance variation,and A is a value greater than zero but not greater than
 5. 10. Theapparatus of claim 4, wherein the time to peak value is calculated as(TTP_(m)+TTP_(b))/A, where TTP_(b) is a selected time value at least asgreat as 0.01 seconds and no greater than 0.1 seconds, and TTP_(m) is ameasured time period between an aortic valve of the patient opening anda peak rate of change of the cardiogenically induced impedancevariation, and A is a value greater than zero but not greater than 5.11. The apparatus of claim 1, wherein the processing unit calculates themean value of the second time-derivative of the cardiogenically inducedimpedance variation as a maximum value of the second time-derivative ofthe cardiogenically induced impedance variation divided by value that isgreater than zero but no greater than
 10. 12. The apparatus of claim 1,wherein the processing unit uses the equation:${SV} = {V_{C} \cdot \sqrt[3]{\lbrack {( \frac{{\mathbb{d}^{2}Z}/{\mathbb{d}t_{mean}^{2}}}{Z_{0}} ) \cdot 10^{- 2}} \rbrack} \cdot T_{LVE}}$to determine the stroke volume of the patient, wherein V_(c) is a volumeof electrically participating tissue of the patient, d²Z/dt² _(mean) isa mean value of a second time-derivative of a cardiogenically inducedimpedance variation of the patient, Z₀ is a quasi-static base impedance,and T_(LVE) is a left ventricular ejection time of the patient.
 13. Theapparatus of claim 12, wherein T_(LVE) is obtained from a dZ/dtwaveform.
 14. The apparatus of claim 13, wherein a trigger forinitiating processing of the dZ/dt waveform is obtained from an R waveof an antecedent ECG waveform or a C wave of an antecedent dZ/dtwaveform.
 15. The apparatus of claim 12, wherein T_(LVE) is obtainedfrom a pulse oximetry waveform (ΔSpO₂(t)), or its first time-derivative,dSpO₂(t)/dt.
 16. The apparatus of claim 12, wherein T_(LVE) is obtainedfrom an applanation tonometry (pressure) waveform (ΔP(t)), or its firsttime-derivative dP(t)/dt.
 17. The apparatus of claim 12, wherein T_(LVE)is obtained from regression equations.
 18. A method of determiningstroke volume by bioimpedance from a patient, comprising: positioningtwo or more spaced apart alternating current flow electrodes on apatient; positioning two or more spaced apart voltage sensing electrodeson the patient and between the alternating current flow electrodes;providing an alternating current flow (I(t)) through the electricallyconductive electrodes creating a current field; measuring a voltage(U(t)) between the voltage sensing electrodes within the current field;and calculating a mean value of a second time-derivative of acardiogenically induced impedance variation of the patient using themeasured voltage (U(t)); and calculating the stroke volume (SV) of thepatient using the calculated second time-derivative mean value.
 19. Themethod of claim 18, wherein the positioning of the alternating currentflow electrodes includes positioning the alternating current flowelectrodes on an arm of the patient proximate a brachial artery, andwherein the positioning of the voltage sensing electrodes includingpositioning the voltage sensing electrodes on the arm of the patientproximate the brachial artery.
 20. The method of claim 18, wherein thepositioning of the alternating current flow electrodes includespositioning the alternating current flow electrodes on a base of thepatient's neck and on a lower thorax of the patient, and wherein thepositioning of the voltage sensing electrodes including positioning thevoltage sensing electrodes on the base of the patient's neck and on thelower thorax of the patient
 21. The method of claim 18, wherein thecalculating of the second time-derivative mean value includes dividing apeak rate of change of the cardiogenically induced impedance variationby a time to peak value of the cardiogenically induced impedance. 22.The method of claim 21, wherein the time to peak value is determined bymeasuring a time period between an aortic valve of the patient openingand a peak rate of change of the cardiogenically induced impedancevariation.
 23. The method of claim 21, wherein the time to peak value isdetermined by selecting a time value at least as great as 0.01 secondsand no greater than 0.1 seconds.
 24. The method of claim 21, wherein thetime to peak value is determined by correcting a rise time between anaortic valve of the patient opening and a peak rate of change of thecardiogenically induced impedance variation.
 25. The method of claim 21,wherein the time to peak value is determined by calculating(TTP_(c)+TTP_(m))/A, where TTP_(m) is a measured time period between anaortic valve of the patient opening and a peak rate of change of thecardiogenically induced impedance variation, TTP_(c) is a corrected risetime between an aortic valve of the patient opening and a peak rate ofchange of the cardiogenically induced impedance variation, and A is avalue greater than zero but not greater than
 5. 26. The method of claim21, wherein the time to peak value is determined by calculating(TTP_(c)+TTP_(b))/A, where TTP_(b) is a selected time value at least asgreat as 0.01 seconds and no greater than 0.1 seconds, and TTP_(c) is acorrected rise time between an aortic valve of the patient opening and apeak rate of change of the cardiogenically induced impedance variation,and A is a value greater than zero but not greater than
 5. 27. Themethod of claim 21, wherein the time to peak value is determined bycalculating (TTP_(m)+TTP_(b))/A, where TTP_(b) is a selected time valueat least as great as 0.01 seconds and no greater than 0.1 seconds, andTTP_(m) is a measured time period between an aortic valve of the patientopening and a peak rate of change of the cardiogenically inducedimpedance variation, and A is a value greater than zero but not greaterthan
 5. 28. The method of claim 18, wherein mean value of the secondtime-derivative of the cardiogenically induced impedance variation iscalculated as a maximum value of the second time-derivative of thecardiogenically induced impedance variation divided by value that isgreater than zero but no greater than
 10. 29. The method of claim 18,wherein the calculating the stroke volume (SV) includes: determining avolume of electrically participating tissue V_(c) of the patient;determining a quasi-static base impedance Z₀; determining a leftventricular ejection time T_(LVE) of the patient; and calculating thestroke volume (SV) of the patient using the equation:${SV} = {V_{C} \cdot \sqrt[3]{\lbrack {( \frac{{\mathbb{d}^{2}Z}/{\mathbb{d}t_{mean}^{2}}}{Z_{0}} ) \cdot 10^{- 2}} \rbrack} \cdot T_{LVE}}$wherein d²Z/dt² _(mean) is the second time-derivative mean value. 30.The method of claim 29, wherein T_(LVE) is determined from a dZ/dtwaveform.
 31. The method of claim 30, wherein a trigger for initiating aprocessing of the dZ/dt waveform is obtained from an R wave or a C waveof an antecedent ECG waveform.
 32. The method of claim 29, whereinT_(LVE) is determined from a pulse oximetry waveform (ΔSpO₂(t)), or itsfirst time-derivative, dSpO₂(t)/dt.
 33. The method of claim 29, whereinT_(LVE) is determined from an applanation tonometry (pressure) waveform(ΔP(t)), or its first time-derivative dP(t)/dt.
 34. The method of claim29, wherein T_(LVE) is determined from regression equations.